Instrumental Variables Estimation of Large Demand Systems with an Application to Fruit and Vegetable Demand and Price Index

The increasing availability of retail scanner data makes it possible to study consumer demand at more disaggregated levels than ever before. This paper derives the asymptotic properties for a tractable iterated three stage least squares (I3SLS) estimator and applies it to estimate a quadratic almost ideal demand (QUAID) system with 47 fruits and vegetables with endogenous prices. Even for a large demand system, the I3SLS is shown to be computationally simple. Then we calculate an exact price index from the estimates and compare it with several commonly used price indexes. We find that the superlative Fisher Ideal and Törnqvist indexes approximate our QUAID exact index well, supporting their continued use in cost-of-living measurement. We also find considerable variation in the regional cost of acquiring fruits and vegetables, suggesting the potential need for adjustment of vouchers for these goods issued by the Special Supplemental Nutrition Program for Women, Infants, and Children